{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%config Completer.use_jedi = False  # for tab auto complete\n",
    "\n",
    "import pyro\n",
    "import pyro.distributions as dist\n",
    "from pyro import sample\n",
    "from pyro.optim import Adam\n",
    "from pyro.infer import SVI, Trace_ELBO\n",
    "from pyro.poutine import trace"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import torch\n",
    "import torch.distributions.constraints as constraints\n",
    "\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "plt.style.use([\"science\", \"notebook\", \"grid\"])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "'1.8.1'"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pyro.__version__"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "def pprint_trace(tr):\n",
    "    \"\"\"\n",
    "    a simple utility to print a trace.\n",
    "    a trace simply executes a DGM by sampling the random variables and stores their values.\n",
    "    \"\"\"\n",
    "    from pprint import pprint\n",
    "    pprint({\n",
    "        name: {\n",
    "            'value': props['value'],\n",
    "            'prob': props['fn'].log_prob(props['value']).exp()\n",
    "        }\n",
    "        for (name, props) in tr.nodes.items()\n",
    "        if props['type'] == 'sample'\n",
    "    })"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exponential-Normal Model (both `Z` and `X` are 1d): it defines the joint $p_{\\theta}(\\bf{x}, \\bf{z})$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "def exp_normal_model(data=None):\n",
    "    lamb = torch.tensor(1.0)\n",
    "    sigma = torch.tensor(1.0)\n",
    "    \n",
    "    z = pyro.sample(\"Z\", pyro.distributions.Exponential(rate=lamb))\n",
    "\n",
    "    pyro.sample(\"X\", pyro.distributions.Normal(loc=z, scale=sigma),\n",
    "                obs=data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Visualize/Render the DGM"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1. if no data is passed, the DGM renders both as unobserved/latent variables"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/svg+xml": [
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       "<polygon fill=\"white\" stroke=\"transparent\" points=\"-4,4 -4,-112 58,-112 58,4 -4,4\"/>\n",
       "<!-- Z -->\n",
       "<g id=\"node1\" class=\"node\">\n",
       "<title>Z</title>\n",
       "<ellipse fill=\"white\" stroke=\"black\" cx=\"27\" cy=\"-90\" rx=\"27\" ry=\"18\"/>\n",
       "<text text-anchor=\"middle\" x=\"27\" y=\"-86.3\" font-family=\"Times,serif\" font-size=\"14.00\">Z</text>\n",
       "</g>\n",
       "<!-- X -->\n",
       "<g id=\"node2\" class=\"node\">\n",
       "<title>X</title>\n",
       "<ellipse fill=\"white\" stroke=\"black\" cx=\"27\" cy=\"-18\" rx=\"27\" ry=\"18\"/>\n",
       "<text text-anchor=\"middle\" x=\"27\" y=\"-14.3\" font-family=\"Times,serif\" font-size=\"14.00\">X</text>\n",
       "</g>\n",
       "<!-- Z&#45;&gt;X -->\n",
       "<g id=\"edge1\" class=\"edge\">\n",
       "<title>Z&#45;&gt;X</title>\n",
       "<path fill=\"none\" stroke=\"black\" d=\"M27,-71.7C27,-63.98 27,-54.71 27,-46.11\"/>\n",
       "<polygon fill=\"black\" stroke=\"black\" points=\"30.5,-46.1 27,-36.1 23.5,-46.1 30.5,-46.1\"/>\n",
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     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data=None\n",
    "pyro.render_model(exp_normal_model, model_args=(data, ))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## example execution of model without data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'X': {'prob': tensor(0.3989), 'value': tensor(0.2333)},\n",
      " 'Z': {'prob': tensor(0.8031), 'value': tensor(0.2193)}}\n"
     ]
    }
   ],
   "source": [
    "tr = trace(exp_normal_model).get_trace()\n",
    "pprint_trace(tr)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8030807577840431"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# just check the prob. values manually! (don't trust ha ha)\n",
    "np.exp(-0.2193)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.3989031859736116"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(1/np.sqrt(2*np.pi)) * np.exp(-0.5 * (0.2193-0.2333)**2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## on passing some data, the `X` nodes get shaded\n",
    "### note: you need to pass the data as a tensor, here `data` is = `[1.3]`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<polygon fill=\"white\" stroke=\"transparent\" points=\"-4,4 -4,-112 58,-112 58,4 -4,4\"/>\n",
       "<!-- Z -->\n",
       "<g id=\"node1\" class=\"node\">\n",
       "<title>Z</title>\n",
       "<ellipse fill=\"white\" stroke=\"black\" cx=\"27\" cy=\"-90\" rx=\"27\" ry=\"18\"/>\n",
       "<text text-anchor=\"middle\" x=\"27\" y=\"-86.3\" font-family=\"Times,serif\" font-size=\"14.00\">Z</text>\n",
       "</g>\n",
       "<!-- X -->\n",
       "<g id=\"node2\" class=\"node\">\n",
       "<title>X</title>\n",
       "<ellipse fill=\"grey\" stroke=\"black\" cx=\"27\" cy=\"-18\" rx=\"27\" ry=\"18\"/>\n",
       "<text text-anchor=\"middle\" x=\"27\" y=\"-14.3\" font-family=\"Times,serif\" font-size=\"14.00\">X</text>\n",
       "</g>\n",
       "<!-- Z&#45;&gt;X -->\n",
       "<g id=\"edge1\" class=\"edge\">\n",
       "<title>Z&#45;&gt;X</title>\n",
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       "<polygon fill=\"black\" stroke=\"black\" points=\"30.5,-46.1 27,-36.1 23.5,-46.1 30.5,-46.1\"/>\n",
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     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data=torch.ones(1) * 1.3\n",
    "pyro.render_model(exp_normal_model, model_args=(data, ))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor([1.3000])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## example execution with any data=`1.3`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{'X': {'prob': tensor([0.2003]), 'value': tensor([1.3000])},\n",
      " 'Z': {'prob': tensor(0.8816), 'value': tensor(0.1260)}}\n"
     ]
    }
   ],
   "source": [
    "tr = trace(exp_normal_model).get_trace(data)\n",
    "pprint_trace(tr)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## note: here the value of `X` would always be sampled as 1.3, so prob. would be just the normal density function evaluated as `X=1.3` and `Z=`the sampled value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.8816148467834161"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.exp(-0.1260)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.2002724612653587"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "(1/np.sqrt(2*np.pi)) * np.exp(-0.5 * (0.1260 - 1.3)**2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Define the surrogate posterior $q_{\\phi}(\\bf{z})$\n",
    "Note $\\phi$ is the parameter of the surrogate distribution. Here it is the rate ($\\lambda$) of the **proposed** Exponential distribution to approximate the posterior $p(\\bf{z}|\\bf{x})$\n",
    "\n",
    "note: In `pyro`, the proposed surrogate posterior is also called the `guide`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "def guide(data=None):\n",
    "    phi = pyro.param(\"phi\", torch.tensor(1.0),\n",
    "                      constraint=constraints.positive)\n",
    "    \n",
    "    pyro.sample(\"Z\", pyro.distributions.Exponential(rate=phi))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
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       "<polygon fill=\"white\" stroke=\"transparent\" points=\"-4,4 -4,-40 58,-40 58,4 -4,4\"/>\n",
       "<!-- Z -->\n",
       "<g id=\"node1\" class=\"node\">\n",
       "<title>Z</title>\n",
       "<ellipse fill=\"white\" stroke=\"black\" cx=\"27\" cy=\"-18\" rx=\"27\" ry=\"18\"/>\n",
       "<text text-anchor=\"middle\" x=\"27\" y=\"-14.3\" font-family=\"Times,serif\" font-size=\"14.00\">Z</text>\n",
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     "execution_count": 11,
     "metadata": {},
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   ],
   "source": [
    "pyro.render_model(guide, model_args=(data, ))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Learn the parameter $\\phi$ using SVI"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "..............."
     ]
    }
   ],
   "source": [
    "# set up the optimizer\n",
    "pyro.clear_param_store()\n",
    "adam_params = {\"lr\": 0.0005, \"betas\": (0.90, 0.999)}\n",
    "optimizer = Adam(adam_params)\n",
    "\n",
    "# setup the inference algorithm\n",
    "svi = SVI(exp_normal_model, guide, optimizer, loss=Trace_ELBO())\n",
    "\n",
    "n_steps = 15000\n",
    "# do gradient steps\n",
    "param_vals = []\n",
    "for step in range(n_steps):\n",
    "    svi.step(data)\n",
    "    param_vals.append({\"phi\": pyro.param(\"phi\").item()})\n",
    "    if step % 1000 == 0:\n",
    "        print('.', end='')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.2721973657608032"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "phi = pyro.param(\"phi\").item()\n",
    "phi"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## manually verify with the derived formula\n",
    "\n",
    "# $\\theta^* = -\\frac{x-1}{2} + \\sqrt{\\frac{(x-1)^2}{4} + 2}$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "x=1.3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [],
   "source": [
    "theta_star = - (x-1)/2 + np.sqrt(2 + 0.25 * (x-1)**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.2721462653327893"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta_star"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "tensor(1.2722, grad_fn=<AddBackward0>)"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pyro.param(\"phi\")"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### convergence plot"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([<AxesSubplot:>], dtype=object)"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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XVxdW156/TgUFBWzfvp2UlJSwdpozZw5z5871GEydSCl7/ABXARLI8Ca9fZ8hwIHAycCTQBvwO5ft/wa2eNhvrP1cl3rYJq3k66+/tvR44YLxUgsVvN5dVCYTL31dJl76uty0vd7r/cLN7cy/fykTL31d3vHWL34dxx8vx+9x9B/ek4mXvi4n3PSBXLJ2m3P7DS8udqZ5+KNi5/r29nbZ2NTqT7Z7JNzKyypU9rLHPaSUgeuHLaXcJqX8WUr5uZTyWuBV4BEhhKMN+w4gWXSuMjtq1jUEmOzswIyCFGqMl1qo4PXJL+WAbazw9JR+PaTeS7i5/fYE23zPS9fXsLupla21vWvt3Vuvipq983e/cYNtKNWN23dz7D3znROmrHeZ+ey7lVud3299/RfSf/8O36/aSl1jC61t7bz+3TqqdlrXEj/cyssqdPEKZkuHn4FEwDHtznIgDsh0S+d40bAi0BkqKSnpOZGCGC+1CHevPc1t/HfpZgAeufRAn/YNN7cpGbb6wNL1NZzy4AKyb/6I5ZtqfT5Ob71WVdj6Xif17cPBboPMnP/Pb4COU4j+WLKN5tY2pJQ8OX81TS3tTH/wSyb+6UMGXvEW1zz7Iyfc90Wv8uKJcCsvq9DFK5gB+xigHqiyL3+O7d32b9zSXQIUywC3EAec7w51w3ipRbh7lW2rZ3dTK5lDExk3vL9P+4ab2/CBCQwfGM+uxhZ+WV/DnpY23lro+7+a3np9Xmi78TksawhRUYJ3bz7Gua14Yy0tre3OqUoHJMTQ0NxGwbqaTv3Id+ze29J8XVU9L3zt3na3d4RbeVmFLl7dBmwhxAwhxAzAMUnqdPu6Y1zStAohnndZ/p0Q4kUhxG+EEMcIIc4RQrwFzADul1I2A0gpq4DHgNuEEH8SQkwVQjwFTANus1bTMzk5OcE4TdAxXmoR7l4VO2yPcYcmx/u8bzi6pSTGdVhevMb3QVV667XNPqTr6FRbX+eT9h9B3SsXMzo1kT0tbSzbUMPWnbZH46fl2kZr+37VVl7+prTb49719lLa2/0foyIcy8sKdPHqqYb9jv1zjX35SfvyPS5pou0fB0XYHns/AszH1lJ8MHCalPLvbse/HbgfuAH4H3AEcL6U8hOfTXpBYWFhME4TdIyXWoS715n/+BqAdVvre0jZmXB0++3xWR2Wl66vobnVtxpYb71KKnYBcOERGR3WH5Rpm9by2HvmO9edkGNrDb1w9Tbe+qEMgKguunjtbGhhpQVDnYZjeVmBLl7dBmwppejiM9UtzeUuywullKdIKYdLKeOklCOklMdLKT/1cPw2KeX9Usp97GknSSnftVKwOxzdA3TDeKlFOHs5GkIBHJjp+1zJ4eh2xbFj+eP08UyfMoKMIf3Y09LG69+tp9XD7GNd0VuvTfZxzUcN7thw70C399kAOfsMBGBBUaVzZrS1c87mxWsPd6aJi4niAvtIc7/79yKSLnuDxz9b2au8QXiWlxXo4hUew+sYDIaw5Mc125zf/++Kg0OYE2t54KIpzLvpGI6yjzn+xxd/4s63CwN6zoamVnbsbia2T1SHyUoAcsd0vhnKHJpI35i9Dy8PyxrCkP59mXFoBneck0N0lOC164/igNG2hnTLNuwA4I63lrJpu/8Tnrzw9VqSLnuDmU987/exDNagXMAWQiCEsGSi8crKSv8zFIYYL7UIN695C8s48x9fUV692zmj1B9O2pch/fv2sGdnws3NnYuPHOP8/sTnq9jT7N2j8d54OZ5WDOnft9NY5geMHsTo1ETn8rybjiE6Kor9Ruxt5Oe6/c9nZFM291xOnjyCyRmdx5j6YMlGn/MHe72e/2oNN7z4EwDv/7SRpesD3ss2oIT7dehOXl6eM9a5olzAdnQgtyJgT5482e9jhCPGSy3Czeu+95bxVfEWxt/0obM7V86ogb06Vri5uXPkfqm8ct2RzuW0372DlJL//LSRxz9byW+fWUhJ5a5O+/XGa3udrcHZ4KS4Ttv6REeRn3cSADmjkpk+ZUSnNK6P0aOihHMq0/09BOz5y3o3D7jD65kvOnaD+qpYrYDnTrhfh+7k5eW5DhjmRLmAbSVFRUWhzkJAMF5qEU5eLa3tlG3b+zh1SWk1APvv07uAHU5uXXH2waP41+UHAdDS1s7+f/6Yy574njveWsqbP5SR+5dPmPnE9yRd9gaPfmyb6qA3XtXdBGyAQYlxrHviHD6//QTnuutPHu/8PqmLMugX18f5Hvvpqw8FIH/FVtZtreuQrmjjDv765i/OfHiiqKiItvZ2ZwO2By6aAkBhWWhq2PV7Wnjlm1Lq9/g377YK16E3RHTAjo6O7jmRghgvtQgnr7JtnluC75s2oFfHCye37rjy2LHEx9ry6jrSmIP3f7I9Ys57ZxlVOxt75bW9zvZIfHA3rxaG9O9L//gY5/J5h+3D41cczHmH7sNpB6R3ud/TVx9KxTPn8ZujxpAxxFYTdzzSdnDnW0uZ899VPPifX7s8TnR0NDX1tj7egxLjOC7b1lgrVAH7rrcL+cPzi8mbt6znxN2gynXYExEdsLOysnpOpCDGSy3CyavUXis7duIwTtw/DYDXrj+SmD69+1cRTm7dIYTo8Gi8O95eWOaT1y/rqvn9sz9y/3u2QNlVDburfF157FheuPaIbmft6hMdRZI90M+58hDAVsvesbuZPc1tXP30Qr4s3gLAvxes6fSoFWBXYwtticOZ/uACAIb0j2PftP70jYmmbNtuauq7rplbTXu77XHws1+uAeCZBSVs9KMhnSrXYU9EdMAuLi4OdRYCgvFSi3Dx2tnQzJVP/gBA5tAkXrnuSObfcQJnHDiy18cMFzdvOGn/tA6127pXLqbulYu59OgxHdJ9u3KrT163vvELr323jk3VtgFoMocmWZPhLpg6cRjHThwGwJvfr+OzpeW8tbCsQ5rb3vilw/LnhZsZ8bt3OOWRRay29xVPHdCXPtFR5IxKBoJXy67c0cCAy9+k/8yO06JO/NOHzP18Va+OqdJ12B0RHbDT07t+xKQyxkstQu21aftu+s98g/Rr3qVuTysAIwf3o19cHw7LGuLXfMyhdvMFIQRnHzwKgEkujewOHtuxj/SS0mpGjOjcKMydTdt3s6yshkUl2zqs99SgzGpmTRsLwF9e/4UnPAS5uf9b3aGW/UlBeac0Q+xdzxz978/8x9c8uyDwY3K/7XZz4cqtb/xCW7v3/eUdqHQddkcg58MOe5qbm3tOpCDGSy1C7fXk/NW4PyF17U7kD6F285V7L5jMrsYWZyMugOOyhxPbJ4q0gfHU72lle10TZdvqGTeu4757mtu46PFv6R8f43zn7c4h4wb7NNtZb3G9KXA0HAS46dQJ/PNT27xKhWU7mGLvw120cUenYzi6nrn2Ef/TKz+zsXo3910wJSD5BljsNm76wH6xHcZOX7xmO4fvm+rTMVW7DrsiomvYVVVVPSdSEOOlFqH2WuwyOMqE9AH86/KDmD7ZmlpgqN18ZVBiHK9cdySnujTwGjm4H9/dezJf3Hmis7b5w8pKijbu4LY3fnH2r/7w540sKKr0GKw/nH0s25+/gP/ednxQPGL7RHcame7z24/n3gsmc9U0253Gc1/Z3g9X7mjgF3s/62fO3RsI0wYmAJ0HdfnXpytJuuwNki57g7VbOnd584XKHQ0dRtOTUrLEHrA/uXUaVx47lu/vm86yh0/nuGzbY/55i8r486s/89c3f6Gl1bvatmrXYVcoF7CtHDglNze350QKYrzUItRejuklNz41g8UPnsqsaeP8egzuSqjdrGJCejLDkuM5ZNwQAB79ppbD7/gvT3y+ij+/+jNSSh77xPOMwPPvOIFp2cOJi4nudeO93vDun6YyzGXCFkdf+tMPtN2MvPJNKVtrGznpgQXONKdPO4R5Nx1D7phBzJxqm/k4c2gSM4/J5FC7uyvXv/BTp3XesrpiJzm3fMSht3/G7ibbq5jy6ga27tzDwH6xHD1+KI9fcTCjBvdjzNAkbjvbNoHH81+t5ekvSpjz31W8lO/dLGWqXYdm4BQPFBQU+J+hMMR4qUUovRqbW2lobiO2TxTJCTE97+AjupXZRUeM7rTuw5838b9lFawo7zj5Rtncc6l75WIOy+oc6IJBSlIcn952HDHRUdx46nhng7ojXB4nf7p0s7Mb2zUnZFFQUMD0KSPIzzuZLPtUqkIInph1CF/ceQIbnjyXS47a2wjv+1VVtLdLFq/Zxul/+5KKmgav8/fdyiqaWtqp2rmHhattNeAVm2sBW79/92B1UObgDkO1Avzz0xVevdNW7To0A6d4ID7e9+kCVcB4qUUovXbY+9wO7BdrWa3aFd3KbMSghA4BD6C1TXLeY984l+85fzJ//80BpPjQfStQZA3vT/ULF3Dv+ZOd6+Jiop0Donxgf3yfnBDDPy7J7bG8BiXG8dTVh1I291znupe+KeX4+74gf8VWfv/cj17nbY3LCHLfr7IF7HJ7S/p9hiR2Sh8VJXjx2iM6rNtU3cCXRVt6PJcu12FENzrLyMgIdRYCgvFSi2B7lVfv5qqnF3Fo1mDOO9R27kGJgQkuOpbZO386hsKSjQxOSWHavfOpt7esB8g7b3/+dNqEEOauM55uxI6033R8vdwW7DJSExFCeF1eKUlxpCTFUV3X1GGAFl/mFncd8vUHew3bMZtZekqCx31Oy02n5oUL6RMteOTj5dz77q98sGSjc8yArtDlOozoGvbKlb2fhi6cMV5qEWyv175bxw+rq3j04xXOMaIHJsYG5Fw6lllSfAxtOzYxPj2ZL+7YO4zoWQeN5ObTJ4YwZ94zaZ+BHfqcO27YfCmvO8+d1Gnd7qZWki57gy21jT3u71rDXrxmO+XVu3n0Y1s7gO5a0sf0iUIIwdH2mdZe/XYdP5d2f6Ogy3UY0QFbl7sud4yXWgTby9HIDOCB921jLJsatm84vLJHDXQOsPLq9UeFNlM+0Cc6ikNd3q07RknzpbyuPHZsh+VolxnI3AdmcaexuZWN1bvpE713n/E3fej8PmxAzzPDuU5IM+3e+d2mDcZ1WLu7mY8LNvWqn7i3RHTArqur6zmRghgvtQi219ade7vROFrnBipgmzILX47cb++7+MS+toDti5fro/Zp2cN46OIDnMvv/riBBb92PWNY1c49SAnDBsTz4EWd+3R7M3Z9QlwfZ0NJKfeO1e6JYJTXrKcXcvHj35F8+Vs0NLX2vEMviOiAXV1d3XMiBTFeahFsryp7wHadrtGX8a19wZRZ+OIYvhQgqa+tOZOvXnfN2J/YPlHcd8EUrjkhizlXHuzcdvYj+WzoYjKZukbb7Fv9E2K4fvp4HrfPlgZw7Yn7MnKwd4PL/PKP0xlon2b0p7VdPxYPdHntaW7rMKVpTHRgQmtEB2zV+uZ5i/FSi2B7Ve20vV/89+8Oc647qYdGO73FlFn44jplquOds69efz5jIpufPo9J9m5Yl08dy/CBe1tkd9UIbZc9YDsexV85bRyvXX8UMw7dh7vP29/r8w/p35cr7cOwLlnbdVAOdHm5znL3zp+OCVh/e+UCtpUDp6jWN89bjJdaBNOrpbWduj2tRAnB4VlD2P78Baz+11k+D/XoLabMwhchBJcdYxsc5ZxD9gF659U3tmPf6J//dprz+6ynF9Le3nlmsDr7/NauDd/OPGgkL157BAlxvnVecoz7vqK8tss0gS4vxyx3J04azskWjBJoBk7xQGJi575+OmC81CKYXnta2gCIj41GCEFcTDRpgzx3obECU2bhzd9/cwDf33uyc9ITK7z6x8fwz5l7H3H/5KEFt+OReFJf/wfrGT/C9r575eadXaYJdHk5AvYYi2ZiMwOneCAtLTCPAUON8VKLYHo5Anac24hRgcKUWXiT2DeG/TMGOZet8nKdfOSXdZ0fVe9qsAXsxHj/A/bYYf2JiY5ifVW980bAnUCU1+6mVjbZ5+h2DEAzbrg1k+Z0RUQH7JKSwE8VFwqMl1oEy+vdH8s45K+fAbYadjAwZaYWVnmNGJTgfBf9l9d/6TDBB8B/7AGuvwUBO6ZPlLOWvbyLx+IrV612Bler+P2zP5Jzy0csXF3lHATGtatZIIjogJ2ZmRnqLAQE46UWwfD6qriSK55c6PzH6T4mc6AwZaYWVnod5dJt7K9u/bIdjbIcgdZfskclA1C8sbbTNikld39Zz4Q/fcjDHxVbcr72dsl/ftpIW7vkpAcWsNP+xODgsSk97OkfER2wdeia4QnjpRbB6HJy5j++7rCutS1wgzu4YspMLaz0OmD03uD11sIyduxupnRrHd+vqqJih61V+qR9rKmROmq2N728pNO2ih2NLNtke8d877u/8uuGznN/+4rrsKoOxo8YQHRUYENqRAfs2traUGchIBgvtQik157mNh79ZHmn9RssfjzYFabM1MJKr5g+UWx8aoZz+V+fruDUh75k+oMLnKPtuU7/6Q+uc3YXuL0zdx8m9aqnF3p93C9+rSDvnUIam1vZ7DITmac+34Ea3tcV4d4KLZwRQkgr81tXV0dSkjWt+sIJ46UWgfJqamlj3xs/oLquCYDHLjuQ179fR8G6Gtt5X7nY8nO6Y8pMLQLh9XHBJi5+/DsyhyY5W1M7qH3pQktqpVJK+s98E4DRqYkseuAU+sX1ob1dMuDyNzulX/LQqeznxeP4CTd9wKbqvYF6+pQRbNu1h59LbTcFN5wynsc/s41TPnxgPCWPn+23iztCCKSUAiK8hq1DX0pPGC+1CJTXPe8ucwZrgMuOyeRflx9MUt8+3HRqcGaUMmWmFoHwOjhzMECnYA1Y9ghZCMFXd58IwPqqem566SfOeyyfwbPedqY5x951DeDLosoej9nW3t4hWAP8d+lmZ7AGuOSoMdxwyngAbg7CLG0RPb1mcnJyqLMQEIyXWgTCa2ttI3P+u8q5fMDoQcTFRDM5YxDr554btG5dpszUIhBeQ5PjGZYc3+nR9ClT/B9gxJWDMgdz1PhUvltZxZs/lHXa/shlB3Li/mlc8+yPvPRNKX84eb9uj7dtV1O32/91+UHsN2IA954/mbMPHtVh5LhAoVwN28qRzlJSAtuiL1QYL7UIhNcSl1rAt/eczII7T3QuBytYgykz1QiU10GZe497zISh/Py3U3nluiMtP8/Hf5nGhPTOj7rvP2ccQ/r3Zap9/PRVm3d6bDjmSuWOrqcI/e9fj2fWtHEAREUJcsek0MfC8cPNSGceKC0t9T9DYYjxUotAeC3bYHtPff30/ZgyelDAxjbuCVNmahEor0PG7Z3KMz42mn3TBgTkxjE6KoojPAyzG99iaxk+YlACCfYxCD79pbzbYznm6x6QEENMdBSL7p/OFceOZe6sQzrMdBYIzEhnHsjKygp1FgKC8VKLQHg53rMdMnaw5cf2BVNmahEor0uPHuP8vqYysFNd3nZ2DmcfPIqX/3CEc90xuXsffz8x6xAA7nq7kO9WbqW9XXYa77y5tY1Z9tbkx2UPp+bFC8keNZD/u+Jg5/jrocBjwBZCpAsh5gghFgkhGoQQUgiR0dPBhBBZQojHhRC/CiHqhRCVQoiPhBCdpl8RQuTbj+v+udF/Le+oqOh6vlaVMV5qYbWXlJIF9kY1E9KTLT22r5gyU4tAebnOt+6p8ZmVDOnfl1euO5JzDtmHksfPovDh06mrqXJuPzZ777Sipzz0JQMuf5MBl79Jk33YXoBVm/c+Lt9e1/277GDSVQ17LHA+sAP4zofjnQgcC7wMnA5cCwwBfhRCeJrf7FfgMLfPWz6czy/q6z3P1ao6xkstrPYqso/21CdaMDo1tJNUmDJTi0B6/eGkfQE448CRATuHO8MHJpA5NKmD1+CkvlxweEantAtcWo67DqV6+zk5Ac2jL3jshy2EiJJSttu/XwU8C4yWUpZ1ezAhBgPVrp2lhRADgDLgYynlZS7r84E+UkqvWx6YftjeYbzUordeX/xaQXVdExceMbrD+g+XbOSSOd9zWNYQ5t9xglXZ7BWmzNQikF5NLW18XLCJ43LSGNgv8IOMuOLJ65VvSvnD84s7rNv23AX0jY3mrR/Wc/Uzi5hx6D68eO0RhJIe+2E7grWvSCm3u0dUKeVOoASwtg2/BZi+lGphvPayq7GFGY9+w9XPLHLOA1y8cQePfbKCS+Z8D0Bi39D32jRlphaB9IqLiWbGoRlBD9bg2euSo8Z0Wpf3TiGwt4Y9pH9cpzShJOCNzoQQg4BsYKWHzVOEEDuFEC32996zAp0fV0zXDLUwXnspq6qn3X5v7BgE4uxH8rl7XqEzzem5wXv02BWmzNQikryiogS/PX4cmUMTucj+lOpn+7CmjvfWQ/r3DV4mvSAYt+BzAAH8y239t8Dr2GrfycBlwHNCiOFSyvuDkC8tH2mB8VKN3ni5DkKxpLSaxubWDuuOyx7GFceOtSR//mDKTC0izevRyw4CoGxbPW/+sJ7Fa7Yzb2EZNfW2gO3aWC4cCGjAFkLcBlwMzJJSrnXdJqW8yy35h0KI/wC3CyH+JaX02PrBvSM5wMyZM5k9ezaxsbGUl5eTnZ1NSUkJbW1t5OTkUFhYyPDhwwGorKxk8uTJFBUVsWzZMi688EKKi4tJT0+nubmZqqoqcnNzKSgoID4+noyMDFauXElGRgZ1dXVUV1c7tycmJpKWlkZJSQmZmZlUV1dTW1vr3J6cnExKSgqlpaVkZWVRUVFBfX29c3tKSgpJSUmUlZUxfvx4ysrKaGxsdG5PTU312Sk6Oppt27ZRVlamlVNWVhYffPABp512mlZOxcXFbN68mYaGBp+cftywt0XrotVb+ebHjtMXHjIiik2bNoXMyXHtzZ8/n1mzZmlRTq5/Tw0NDZSVlWnllJubywcffMBhhx2mlVNBQQErVqzg3HPP7dKpX79+zr+dWU8vZL+htpp1XFQb+fn5QXGaM2cOc+fO9RT29sa/nhpx+dLozG2/a4CngDuklA94uc/5wNvA4VLKRR62W9robOvWrQwdOtSy44ULxkstfPX616cruPPtwg7rMob0o2ybbQauAzNTeO/mqWFROzBlphaR7HX3vEIe+2RFh3Uf/PlYjssZHsis9UjAJ/8QQlwKPAk86m2wdiMoU4iVlZUF4zRBx3iphS9eLa3tnYI14AzWJ+6fxtd3nxQWwRpMmalGJHvdc/5kbjl9Yod1AxJiApSj3mF5wBZCnA28CDwnpbzFx91/AzQCRVbnyxONjV2PFasyxkstuvKqa2xh8ZpttLXv7bRx+ZM/dEjjPm7yqwEYn9kfIq3MVCfSvdz7ZyeHoEV7d3QZsIUQM4QQMwDHgCfT7euOcUnTKoR43mX5aOBNYBnwkhDiUJfPFJd0RwkhPhVCzBJCHCeEOEcI8SFwBnCPlHK3xZ4eyc31NJaL+hgvtfDkJaXkgn99w/H3fcHjn9lm3Wpvl3z086YO6W49K4fcMYMAeOvGo0mIC31XLlciqcx0INK99k3rT9bw/gBECcGIQQmBzJbPdFfDfsf+uca+/KR9+R6XNNH2j4NpQBxwAPADsMjl8x+XdJX2c98LfAa8gm1EtIullH/vpYvPmL6UahFJXiWVu/hupW04xY8LNiGl5OpnFjq333FODmcdNJJTpowgP+9k6l65mFMPSA9anr0lkspMByLdSwhBwd9P44XfH86395xEfGx43QB3mRvHS+7ucE8jpcwD8rzYby0wvefsBZbU1MDOuBIqjJdapKamUlPfxJTZn1BT38RPD57CwX/9zLl96foaFq/dzrxFG5zr/nJW+AyX2B06l5mOGC8b5x2WEZiM+El43T4EmdjY8Ho/YRXGSy1iYmLY59r3nMuuwRqgrV1ywn1fOJejo3q8lw4bdC0z46UWunhF9PSa5eXdz4eqKsZLLYrXbuxy210zJnVa9+YNRwcyO5aia5kZL7XQxUu5gC2EQAhBXl6e38fKzs72P0NhiPFSizUNyQDEx0Y75+oF2PTUjE4zG/3t4gOYPiXshuXvEl3LzHiphWpeeXl5zljninKPxK0cOKWkpITBgwdbdrxwwXipxbfFtpbf2SOTmXlMJjOPyXRuS+4Xy5KHTmVQYiwVOxqZNGpgqLLZK3QtM+OlFqp55eXlOSulrkFbuYBtJW1tbT0nUhDjpRY1DTavm90GbXCw3whbX+vUAfFBy5NV6FpmxkstdPFS7pG4leTkqNHS1leMV/B44eu1JF32BkmXvcF7P27oeQc3pJRsrLX9M9lncL8eUqtHOJaZFRgvtdDFK6IDdmFhYaizEBCMV/C44cWfnN//8noBTS2+3cn/7YNidja2ApCSFB7DiVpJOJaZFRgvtdDFK6IDtmPWF90wXsHhpfwOE9Cxdece3lvsWy377x8WO78PVfCRd0+EW5lZhfFSC128IjpgGwz+8MhHywE4cEwKj152IAD/K6zwev9Vm3fS1m5rRPnitYcTpVD/aoPBEHwiOmBXVlaGOgsBwXgFnu11e9i8owGAp64+lGMnDgMgf8XWDpN1dEfBumrn93MP2cf6TIYB4VRmVmK81EIXr4gO2JMnTw51FgKC8QosXxZVcsDsT2htkwxOimO/EQMYOyyJjCH9qKlv4u2FZV4dZ8fuZgCuPCajU39LXQiXMrMa46UWungpF7CtHDilqCgos3gGHePlP00tbcxfVkFLa8fa8totuzjr4a+dwdYxiIkQgkuOGgPAPz4sZnNNA2f94ysm3fIR/15Q4nH8gFr7MZrqagKpElLMtagWxis8MAOneCA6OrrnRApivPznppeX8Oq36wB48qpDuPRo22Amj368okO6mOi997w3nz6RN39YT+nWek66/ws2bLfNEnvzKz+TkhjHuYd2fOy9Y3cTAAPilfsz9BpzLaqF8QoPuho4RbkatpVkZWWFOgsBwXj5z8LVVc7v1z63mBmP5iOl5Ke12zukmzgy2fm9T3QUFx0xGsAZrB08/PHyTjebO+ptNexxGeoMNeor5lpUC+MV3kR0wC4uLu45kYIYr97z7o9l3PTSEqrrmjqs/9+yCt79cQNrt9QRJQRr/+9snvntoVwxdWyHdO5jfztYvqmWr5dvAeDXDTu47Y1feMc+0Ept1eYAmIQH5lpUC+MV3kR0wE5PTw91FgKC8eodbe3t3PDiEp77ag21DS0AfPDnY53bb3jxJ9qlZOywJIYmx3PxkWOI6dPxT2h8ejL3XzgFgBP3T2NwUhwHZqYA8I59PutZTy/kic9XOffJ3VfP8gJzLaqG8Qpv9H155gXNzc2hzkJAMF694+fSanY1tnRYd1zOcDY/cx4jfvcOdXtsI5JluzwG98QNp4znhlPGA7Y2F4VlOzj67s9ZVFJFc2sbqzbvdKY9duIwhibqe99srkW1MF7hjb7/Kbygqqqq50QKYrx6x5otdR2Wzz1kFAD942M4LnuYc31yv1ivjymEcAb40q31pFz5tnPbWQeN5PU/HqVteYG5FlXDeIU3wspW14FGCCGtzG9dXR1JSUmWHS9cMF6+s3bLLp74fBXPf7WWP04fz/0XTu7QOnPH7mZG/f5dAObddIzPc1InXfZGh+XDsoYw/44TAH3LC/R1M15qobKXEAIppYAIr2EXFBSEOgsBwXh5T+WOBrbWNnLUXZ/z/Fe2scGHJfft1P9xYL9YNj41g49mT/M5WAMsvH86/eNjnMuXT90757Wu5QX6uhkvtdDFS7l32I5/pHfffbffg6fEx+s32QIYL2/Y2dDM6D+8T0tb52FEu5qEY2C/WI51eTTuCzmjBrL5mfOo3d2MtB/Lga7lBfq6GS+1UM0rLy+Pe+65p9P6iH4kvnXrVoYOHWrZ8cIF49U9rW3tTLrlIzZVN3jc/t+/HseR+wXv96dreYG+bsZLLVT2Mo/E7axcuTLUWQgIxqt7bnxpSZfBGiBzaHDfdelaXqCvm/FSC128lHskbiUZGRmhzkJAMF5d094ued8+Z3Xeeftz+dSxnPLQArbXNfHezVPZ3dTK8IEJfp/HF3QtL9DXzXiphS5eER2w6+rqek6kIMara9Zs2eXsT33jqeOJjori23tOpl1K4mND8+ega3mBvm7GSy108YrogF1dXd1zIgUxXl1TUrkLgBMmDSc6yvZGKC4mtBMD6FpeoK+b8VILXbwi+h12bm5uqLMQEIxX16yptN1pjxvW3+9jWYWu5QX6uhkvtdDFK6IDti5989yJJK/1VfUcccd/ue/dZd3u6+hdsHaLrYY9bnj4BGxdywv0dTNeaqGLV0Q/Ek9MTAx1FgJCJHm9s6iMXzfu4NeNO0gblMCsaeM6pVlZXstJDywgY0iic7KOfYb0C3h+vUXX8gJ93YyXWujipVwNWwiBEMLvQVMA0tLS/M9QGBJJXq7zTt/40hJmv/ZzpzSvfbeeHbubWVpW45zPesSg4LYE7w5dywv0dTNeaqGaV15enjPWuaJcwJZSIqW0JGCXlJT4n6EwJJK8djV0nIXnqfklLF1f02HdwtWdB/4Pp4Cta3mBvm7GSy1U88rLy3PGOleUC9hWkpmZ2XMiBYkkL8d0mO/fMpXzD9sHgGueXcRnS8uRUrKmchc/r6t2pgFIH5TAgATvZ9wKNLqWF+jrZrzUQheviA7YujT1dyeSvHY12AJ2//gYHrr4AABWlO/kgn9+yxvfr2fu/1YBkDtmECdMSmPXyxex8l9nBS3P3qBreYG+bsZLLXTx8hiwhRDpQog5QohFQogGIYQUQmT0dDAhRJYQ4nEhxK9CiHohRKUQ4iMhxP5dpL9aCLFKCNEkhFgthLjGTx+fqK2tDebpgkYkeO3Y3cxT81c7a8+DEuNIHRDP5IyBzjS3vfELi9fY3llffOQYgE7vhMIBXcsL9HUzXmqhi5fHyT+EEFOBt4ECIBo4ERgtpSzr9mBCXAf8FngZ+AVIBmYDk4EjpZQFLmmvBp4BHgIWAMcBfwX+IKV8qovjm/mwvUB3Lyklab97h3r7iGWTRg3k+/tORgjB5poG/vFhMcs21FCwbu+77B8fOIWJI5NDlPPu0bW8QF8346UWKnt5M/nHt1LKoVLKU4B3fDj2W8D+UspHpZRfSyn/A5wM7AFucMlAH+AB4FUp5e32tHcALwH3CSFiPBzbcnTpm+eO7l6f/FLuDNYA10/fz1lzHjEogcevOJjHLjuImOi9l3daGDUyc0fX8gJ93YyXWuji5TFgSyk7TxLsBVLK7e5VYCnlTqAEGOGy+jBgCPCa2yFeBVKAI3tzfl9JTk4OxmmCju5e85dVALbBT76860QuODyjU9oDxqRw4RF71ycnBOUesFfoWl6gr5vxUgtdvALe6EwIMQjIBlznN5to/1nslny5/eeEQOcLICUlJRinCTq6e/26YQcA/3fFwRw8dnCX76VvP2cSUzIG8dezc8Ly3bUDXcsL9HUzXmqhi1cwRjqbAwjgXy7rBtl/7nBLW+O2vROe/vHOnDmT2bNnExsbS3l5OdnZ2ZSUlNDW1kZOTg6FhYUMHz4cgMrKSiZPnkxRURHLli3jwgsvpLi4mPT0dJqbm6mqqiI3N5eCggLi4+PJyMhg5cqVZGRkUFdXR3V1tXN7YmIiaWlplJSUkJmZSXV1NbW1tc7tycnJpKSkUFpaSlZWFhUVFdTX1zu3p6SkkJSURFlZGePHj6esrIzGxkbn9tTUVJ+doqOj2bZtG6WlpVo5ZWVl8d5773HKqadSvNF22Ywe1If8/Pxune6d1pfExCYqKirC0qm4uJjNmzczZcoUbcrJ9e9p/vz5zJo1SyunqqoqGhoaKC0t1copNzeX9957j8MOO0wrp4KCAlasWMG5554b1k5z5sxh7ty53QZTj43O3ALkVcCzeNHozMO+twEPArOklC+4rP8rtnfY8VLKPS7r+wAtwF1Syvs8HM/SRmcVFRXKjYDjDTp7xQ8YzKjfv0v/+Bg2P3NeqLNkCbqWF+jrZrzUQmUvbxqdWXGSa7AF6ztcg7UdR816oNt6R826hiBQUVERjNMEHV29flpRxjuLygBI7hc+A5/4i67lBfq6GS+10MUrII/EhRCXAk8Cj0opH/CQxPGueiJQ6bLe8e56RSDy5U59fX0wThN0dPSqrmvi0lfKgDIA4mNDO4e1lehYXg50dTNeaqGLl+U1bCHE2cCLwHNSylu6SLYI2A78xm39Jdhq1z9YnS9P6DJHqjs6en1euLnD8uqKXSHKifXoWF4OdHUzXmqhi1eXAVsIMUMIMQNwmE63rzvGJU2rEOJ5l+WjgTeBZcBLQohDXT5THOmklC3AncBMIcT9QoipQoh7gSuxvb/uOKNDgNClb5474e61u6mVDds63vG2t3ffNmFJqW3Esigh6B8fw8OX6PEHCOFfXv6gq5vxUgtdvLp7JO4+YMqT9p/fAFPt36PtHwfTgDjgADrXkjcAGY4FKeXTQggJ3Az8GdgIXCelfJIgoUtTf3fC3eucR75m4eptTByZzNd3n8gnBeXc9PIS7jl/ssf5rAEWlWwD4PU/HsVpuenBzG7ACffy8gdd3YyXWuji1WXAdrRK6w73NFLKPCDP25NLKZ/BNjxpSFB1qLqeCFcvKSWXPfE9C1fbgu/yTbW8++MGPliyiZ0NLdz40hIuOmI00VGCuJi994G7m1pZUb6TPtGCE/cfHqrsB4xwLS8r0NXNeKmFLl4RPVtXWVlZqLMQEMLVq6RyFx8s2dRh3YJfK50zbgGc/MAChl49j7cXrmfd1jqklM7H50P7RRHbR5/GZg7CtbysQFc346UWungpF7CFEAghyMvL8/tY48eP9z9DYUggvKSUzFtYxtsL1/f6GOXVDc7vD15ka9Lw/k8b+XHNNuf6pWU1tLVLrnp6Efv/+WMe+Xg5tbttTRqGDkzs9bnDGV2vQ9DXzXiphWpeeXl5zljninIBW0qJlNKSgK3LXZc7gfB6+ZtSZj29kKueXkTab+fx2Ce+9byTUlJeYwvYFx2RwfXTx3PNCVkd0kRHdX4L88Tnq2losk30IdqD0hYx6Oh6HYK+bsZLLVTzysvLc8Y6V5QL2FbS2NgY6iwEhEB4fbNiq/N73Z5W7p5XSGGZd+PbtLdLjrn7f1z3/GJg78xZ5xyyjzONEPDtPSeTMyqZ47KHOdfX1Dexvsr2SLyPsG6Uu3BC1+sQ9HUzXmqhi1cwxhIPW3Tpm+dOILxKt9R1WvfpL+VMzuhy2HcnZdvqWeoS3PvH20YpO3js3pabUsKkfQay8P5TkFLyy/oa7nq7kG9XbuXL4i0ApKXq0dLTHV2vQ9DXzXiphS5eEV3D1qVvnjtWezU2tzoD7hs3HOVcv6CosqtdOuCYDtPBCZNsLb2jo6Kctek+0XsfhwshyB2TwjEThgK2GwOA3bvc54rRA12vQ9DXzXiphS5eER2wU1NTQ52FgGC112e/2EYZSxsYz2kHpFP57/OI7RPFz6XVLPi1gt/9exEfurX+duWr5bYacs6oZD7487HkjNo7hPwTsw5h9hkTWffEuZ32u+DwjA7vtQf2T7BKKazQ9ToEfd2Ml1ro4hXRATs2Vp8JJFyx2mvxWlsr7gsOH40QgsS+MUydaKsZn/1IPm98v55L5nzHtl17Ou3b1t7ufNf94rVHcFxOx37U6Sn9uHPG/gz0MJnHPkMSOXH/vTPsJMTFWOYUTuh6HYK+bsZLLXTxiuiAXV5eHuosBASrvX5aaxsWdJpLY7B7ztu/U7prnv2x07pfN9RSuaOREYMSGDvM98ELbj0z2/m9aENQJnELOrpeh6Cvm/FSC128IjpgZ2dn95xIQaz02lzTQNHGWsDWKMx5jlEDWfWvs/jHJbm8ct2RgO1d9WKXPtUbttUz6+mFgO1xeHSU75fbAWNSyBxq6399/pFje6sR1uh6HYK+bsZLLXTxUi5gWzlwSklJif8ZCkP89ZJS8swXq7l0znfsd+MHNLe2A3R6bD1iUAK/P3Ffzj54lHN87ze+3zuwynXPL2ZNpW1Wre11Tb3Oz89/O40v7jyB7P56TJHnjq7XIejrZrzUQjUvM3CKB9ra2vzPUBjir9fVzyzillcLOg0j6n7xuHLHOZMA+M9PG9ltH+gk36Xv9o2n9H6koT7RURw6bgjI9l4fI5zR9ToEfd2Ml1qo5tXVwCkR3Q87Jycn1FkICP56eepz7dr4yxMTRyYzIX0AK8p3MuzqeZw4aW/jsvVzz2FwUl+/8gSmvFREVzfjpRa6eClXw7aSwsLCUGchIPjj1dzaxq8bbf2dV/3rLCqeOY9NT83grRuO7nHf8w7LcH6f/6utj3bOqGRLgjWY8lIRXd2Ml1ro4hXRAXv4cP2magT/vNZtrae5tZ0xqYmMGJRAUnwMyf1iienT86Uy49B9Oq373Qn79jov7pjyUg9d3YyXWujiFdEB29CZ0q22x+GZveiClTEkkQ9nH8sd5+x9/JQzMtmqrBkMBkNEE9EBu7LSu6E1VcMXr7rGFp75YjWVO2wzaZXYW3VnDu3dhO/Tsodz02kTGDe8P/vvM7DDqGb+YspLPXR1M15qoYtXRDc6mzx5cqizEBB88Xr6i9Xc++6vzP3fan595AxnN6x90wb0+vyxfaL5+aFTaZeSPtHW3ROa8lIPXd2Ml1ro4hXRNeyioqJQZyEg+OJVWGZrYLa+qp6ky97g1W/XAbY+1v4QFSUsDdZgyktFdHUzXmqhi5dyAdvKgVOio6P9z1AY4otXWZXnwUjSBsZblR3LMOWlHrq6GS+1UM2rq4FThHvH7HBGCCGtzO/27dsZPHiwZccLF7z1am+XDP/tPBqa2zjv0H1458cNAExIH8DC+6f3aijRQBLp5aUiuroZL7VQ2UsIgZRSgII1bCspLi4OdRYCgrdelbWNNDS3MTgpjheuPYK6Vy6m7pWLWfzgqWEXrMGUl4ro6ma81EIXr/D7rxxE0tPTQ52FgOCt19ottgZmY4f1D2R2LCPSy0tFdHUzXmqhi1dEB+zm5uZQZyEgeOu1ptLW53rc8N514Qo2kV5eKqKrm/FSC128IjpgV1VVhToLAaEnr6aWNmp3N7Nq805AnRp2pJaXyujqZrzUQheviG50VldXR1KSGrVLX+jOa1lZDUfe9XmHdZ/ffjxH7JsajKz5RSSWl+ro6ma81EJlL9PozE5BQUGosxAQuvN6/uu1ndYdnjUkkNmxjEgsL9XR1c14qYUuXhEdsOPjw6+vsRV057W5pqHD8oFjUrqd5zqciMTyUh1d3YyXWujipVzAtnLglIyMDL+PEY5057Xa/t76d8dnkTk0kVevPzJIufKfSCwv1dHVzXiphWpeXQ2colzAllIipbQkYK9cudL/DIUhXXlV1zWxYftu4mKieOCiKRQ+fAbpKf2CnLveE2nlpQO6uhkvtVDNKy8vzxnrXInoyT9Uu+vyFnev71Zu5ZI531NT3wTA/vsMIi5GraH6IHLKSyd0dTNeaqGLV0QH7Lq6ulBnISC4ejU2t3LKQ1922H7kfuHfItwTkVBeuqGrm/FSC128PD4SF0KkCyHmCCEWCSEahBBSCJHhzQGFEH8SQnwshKi075fXRbqX7NvdP//qtY2PVFdXB+tUQcXVa1HJtk7bLzpidDCzYxmRUF66oaub8VILXbw89sMWQkwF3gYKgGjgRGC0lLKsxwMKsRLYBfwCXAPcI6XM85DuJeAU4Ay3TZVSyg1dHNv0w/aCuro63v5pCze9vMS5buYxmexsaGZgYhz/d8XBIcxd79G5vHT0An3djJdaqOzlTT/sb6WUQ6WUpwDv+Hj8iVLKQ4DrvUjbLKX80e3jMVgHAl365rnz1Q8/dQjWAOccMopXrz9K2WAN+paXrl6gr5vxUgtdvDwGbClle28P6M++wSYxMTHUWQgIpbWdi/XgsWpOLeeKruWlqxfo62a81EIXr1A3OksVQmwHkoF1wPPAI1LKtmCcPC0tLRinCTorttt+/um0CcRER5E2KIHEvjGhzZQF6FpeunqBvm7GSy108QplwC7E9o58OdAXOBt4CBgHXNXVTp5G5Zo5cyazZ88mNjaW8vJysrOzKSkpoa2tjZycHAoLCxk+fDgAlZWVTJ48maKiIpYtW8aFF15IcXEx6enpNDc3U1VVRW5uLgUFBcTHx5ORkcHKlSvJyMigrq6O6upq5/bExETS0tIoKSkhMzOT6upqamtrnduTk5NJSUmhtLSUrKwsKioqqK+vd25PSUkhKSmJsrIyxo8fT1lZGY2Njc7tqampPjtFR0fz3cotAOyfCvul9qGqqpy6uqFKO2VlZTFv3jxOO+00bcopKyuL4uJiNm/ezJQpU7Rycvw9zZ8/n1mzZmnlVFVVRUNDAyUlJVo55ebmMm/ePA477DCtnAoKClixYgXnnntuWDvNmTOHuXPndhs0e5z8QwhxFfAsXjY6c9mvD9BCF43Outjnn8CNQJaUco2H7ZY2Otu0aRMjR4607HjhwK7GFtKveYc+UVFU/vs8Jftbd4WO5QX6eoG+bsZLLVT2CufJP960/zwwGCfTpam/K/e9uwwpYXRqolbBGvQsL9DXC/R1M15qoYtXuAVsB0GZ87O2tjYYpwkq36+yzfs6deLQEOfEenQsL9DXC/R1M15qoYtXuAXs32AL1kt6SmgFubm5wThN0FhTuYviTbXERAvuv3BKqLNjObqVlwNdvUBfN+OlFrp4dRmwhRAzhBAzAIfpdPu6Y1zStAohnnfb70D7fufYV01wHEsIkWBPs48Q4lshxLVCiBOFEKcLIV7A1nf7GSllqZWSXaFL3zwHjtr1oaPiiI8NdQcA69GtvBzo6gX6uhkvtdDFq7v/6u4Dpjxp//kNMNX+Pdr+ceU6YKbL8nn2D8BooAyoA2qAvwBDgXZgFfBHl/MEnOTk5GCdKihU7WwEbO+vdUS38nKgqxfo62a81EIXry4DtqNVWnd4SiOlvBy4vIf9aoCzesxdgElJSQl1Fixl2y7bbFwjBvcPcU4Cg27l5UBXL9DXzXiphS5e4fYOO6iUlgblyXvQ2LZrDwDN9TUhzklg0K28HOjqBfq6GS+10MVLuYAthEAIQV5ent/HysrK8j9DYcJL+Wt5/6eNAOw3Rs3+hj2hU3m5oqsX6OtmvNRCNa+8vDxnrHNFuYAtpURKaUnArqio8D9DYcDK8lquf+En53JTfW3oMhNAdCkvd3T1An3djJdaqOaVl5fnjHWuKBewraS+vj7UWbCEj37e1GE5Mao5RDkJLLqUlzu6eoG+bsZLLXTx6nFo0nDCzIftmbMf/poFRZUA5J23P7+dOkoLL3d0KS93dPUCfd2Ml1qo7BXOQ5MGFV365hWW2RqZrXjsTG4+faI2Xu4YL/XQ1c14qYUuXhEdsHVo6t/S2s72uiaihCBtUDygh5cnjJd66OpmvNRCF6+IDtiqPiJxZXudrSvX4P5xREfZilMHL08YL/XQ1c14qYUuXhEdsMvKykKdBb/ZutMWsFP793Wu08HLE8ZLPXR1M15qoYtXRAfs8ePHhzoLflPlCNgD9gZsHbw8YbzUQ1c346UWungpF7CtHDhFh7uuql2mhq06unqBvm7GSy1U8+pq4BTlpnSysltXY2OjZccKFTX1tvHDU5LinOt08PKE8VIPXd2Ml1qo5pWXl+eslLoGbeUCtpWoOEfq5poGLp3zHUtKq7nz3EmsrtgJwKDEvQFbRS9vMF7qoaub8VILXbyUeyRuJSr2zXMEa4D73vuVeYs2ADB14jBnGhW9vMF4qYeubsZLLXTxiuiAnZqaGuos+MTG7budwdqVuJgoDhyzt5+hal7eYrzUQ1c346UWunhF9CPx2NjYUGfBJ74qtg0/OmJQAh/9ZRpbdjSydmsdlx41hqiove85VPPyFuOlHrq6GS+10MUromvY5eXloc6CT3xdvAWAm0+bQNbw/hw9YShXHjuWmD4di1E1L28xXuqhq5vxUgtdvCI6YGdnZ4c6C14jpSR/xVYAjs0e1m1albx8wXiph65uxkstdPGK6IBdUlIS6ix4TXl1AzX1TaQkxZE5tPth9lTy8gXjpR66uhkvtdDFS7mAbeXAKW1tbf5nKEhs2L4bgLHDkjp1pndHJS9fMF7qoaub8VIL1by6GjgloufDrq2tJTk52bLjBZJ3fyzjiicXctZBI3n1+qO6TauSly8YL/XQ1c14qYXKXmY+bDuFhYWhzoLXbNtlG9FsiMsQpF2hkpcvGC/10NXNeKmFLl4RHbCHDx8e6ix4jWMI0sEuQ5B2hUpevmC81ENXN+OlFrp4RXTAVolt9kk+UrwI2AaDwWDQj4gO2JWVlaHOgtcUltUAMKaHFuKglpcvGC/10NXNeKmFLl6m0ZkCDRF2N7Uy4nfvAFD+9AwS+8Z0m14VL18xXuqhq5vxUguVvUyjMztFRUWhzoJXLF1fTVu7ZGJ6co/BGtTx8hXjpR66uhkvtdDFK6IDdnR0dKiz4BULV28D4NCswV6lV8XLV4yXeujqZrzUQheviA7YWVlZoc6CVywosr1/OSjTu4CtipevGC/10NXNeKmFLl7KBWwrRzorLi72P0MB5tcNO1hUYqth57pModkdKnj1BuOlHrq6GS+1UM2rq5HOlJte08pGZ+np6ZYdK1A8/9UaAE6cNJxxw/t7tY8KXr3BeKmHrm7GSy1U88rLy3NWSl2DtnI1bCtpbm4OdRa6pb1d8skvtmnh7j5vstf7hbtXbzFe6qGrm/FSC128PAZsIUS6EGKOEGKREKJBCCGFEBneHFAI8SchxMdCiEr7fnndpD1LCLFUCLFHCLFBCHGHECJorQOqqqqCdapesaK8lqqdexgxKIGcUcle7xfuXr3FeKmHrm7GSy108eqqhj0WOB/YAXzn4zGvBlKBD7pLJIQ4CXgPWAJMBx4H7gAe9PF8vSY3NzdYp+oV362yXWSHjB3c4wxdroS7V28xXuqhq5vxUgtdvLoK2N9KKYdKKU8B3vHxmBOllIcA1/eQ7m/A91LK30opv5ZSPoYtWN8khBjm4zl7RUFBQTBO02tmv2bL38FjvWsd7iDcvXqL8VIPXd2Ml1ro4uUxYEsp23t7QG/2FUKMBCYDr7ltehWIwVbjDjjx8fHBOE2vKN64w/n9nENG+bRvOHv5g/FSD13djJda6OIVqkZnE+0/O7S1l1KuBxqACcHIREZGRjBO0yve+XEDAAdmpjB8YIJP+4azlz8YL/XQ1c14qYUuXqEK2IPsP3d42LbDZXtAWblyZTBO0yu+t7+/nn1Gts/7hrOXPxgv9dDVzXiphS5eyvXD9tT4aubMmcyePZvY2FjKy8vJzs6mpKSEtrY2cnJyKCwsdM6HWllZyeTJkykqKqK6uprt27dTXFxMeno6zc3NVFVVkZubS0FBAfHx8WRkZLBy5UoyMjKoq6ujurrauT0xMZG0tDRKSkrIzMykurqa2tpa5/bk5GRSUlIoLS0lKyuLiooK6uvrndtTUlJISkqirKyM8ePHU1ZWRmNjIwcccADLN1YDMEjsIj9/jddO0dHR9O/fn/z8/LBycmxPTU31uZyio6PJyspiy5YtrF27Visnx4AOK1as0MrJce1t2bKFuro6rZyqqqoYPHgw+fn5Wjnl5uayZcsWFi9erJVTQUEBO3bsYOvWrWHtNGfOHObOndt9/OtpIBIhxFXAs8BoKWVZt4k77tcHaAHukVLmuW2bDnwGHC6lXOS2bTfwpJTyzx6OaelsXUVFReTk5Fh2PKsor97N+Js+ZGC/WDY8ea5PLcQhfL38xXiph65uxkstVPYKh9m6ltt/TnRdae/rnQCsCEYmqqurg3Ean1lSastX7pgUn4M1hK+Xvxgv9dDVzXiphS5eIQnYUsqNwDLgN26bLsFWK/9vMPIRrn3zFq+xjR3ua3cuB+Hq5S/GSz10dTNeaqGLV5cBWwgxQwgxA3CYTrevO8YlTasQ4nm3/Q6073eOfdUEx7GEEK7Nnf8KHCOEeEYIMVUIcRO2gVMel1JusUKuJ8K1b56jhn1QpneTfbgTrl7+YrzUQ1c346UWunh11+jMfcCUJ+0/vwGm2r9H2z+uXAfMdFk+z/4BGA2UAUgpP7MH9ruBy4Gt2AZOecDbzPtLYmJisE7lNU0tbRSW1QBwoJfTaboTjl5WYLzUQ1c346UWunh1GbAdL7m7w1MaKeXl2AJwj0gp3wfe9yZtIEhLSwvVqbtk+aZamlvbyRren+R+sb06Rjh6WYHxUg9d3YyXWujiFdGzdZWUlIQ6C50oWGd7HH7A6N53RQ9HLyswXuqhq5vxUgtdvCI6YGdmZoY6C534ae12AA7qZYMzCE8vKzBe6qGrm/FSC128lAvYQgiEEM7Jvf0hHJv6OwJ2b1uIQ3h6WYHxUg9d3YyXWqjmlZeX54x1rig30pmVA6fU1tZadixvqahpYMrsj8lITeTOc/cnbWA8T39RwqkHpJM2KJ51VfUkxEYzMT251+cIhVcwMF7qoaub8VIL1bzy8vKclVLXoN3jSGfhhNUjndXV1ZGUlGTZ8bzhjL9/xdfLbb3WoqMEIwYlsHH77g5pDssawvw7Tuj1OULhFQyMl3ro6ma81EJlr3AY6SwsCHbfvN1Nrc5gDdDWLjsFa4DxIwb4dR5d+hy6Y7zUQ1c346UWunhFdMBOTk4O2rmklFz19EIABvaL5dNbj3Nui4+N5pNbpzmXByb2rjuXg2B6BRPjpR66uhkvtdDFK6IDdkpK70YS6w0/rK7ik4JyAM47bB+OGp/q3LanpY1jJgzj3ENGER0lOPPAUX6dK5hewcR4qYeubsZLLXTxiuiAXVpaGrRzffTzJuf3y6eORQjBxUeOBuDq48YB8NTVh7LisTOZ4kcfbAiuVzAxXuqhq5vxUgtdvJRrJW4lWVlZQTvX/GWVACy48wRyRg0E4PHLD+aIfVOZPmUEAPGxfYgf5H+RBNMrmBgv9dDVzXiphS5eEV3DrqioCMp5ttQ2Urq1jn5xfcgds/fRTN/YaC47JpMh/ftaer5geQUb46UeuroZL7XQxUu5gG3lwCn19fX+Z6gHmlvbGPfH/wAwYlACfaID/ysPhlcoMF7qoaub8VIL1by6GjjF9MMOcN+8YVfPY3dTKwCPX34QV04bF9Dzgdp9DrvDeKmHrm7GSy1U9jL9sO0Eum/era8XOIP1GQeODEqwBn36HLpjvNRDVzfjpRa6eEV0wA5kU/+ybfXM/d9q5/Jz1xwWsHO5o0sXBneMl3ro6ma81EIXr4gO2IF8RLK2cpfz+5KHTiU+NngN8lV99NMTxks9dHUzXmqhi1dEB+yysrKAHXvzjkYALjpiNPv5OdSorwTSK5QYL/XQ1c14qYUuXhEdsMePHx+wY6/bWgdA2qD4gJ2jKwLpFUqMl3ro6ma81EIXr4gO2IG86/pu5VYAckYODNg5ukKXu0l3jJd66OpmvNRCF6+IDtiNjY2WHKeusYXPlpbT1t4OwHs/bmBJqW3C9KMnDLXkHL5glVe4YbzUQ1c346UWungpF7CtHDglNzfX72Ms31RL2u/e4YJ/fsvtby6lsKyGy5/8AbDNdz04Kc7vc/iKFV7hiPFSD13djJdaqObV1cApygVsKSVSSksCthV98x7/bIXz+9z/reaouz53Lj8x65BOv/BgoEufQ3eMl3ro6ma81EI1r7y8PGesc0W5gG0lqampPSfqgcKyHQCMHdax28BTVx/KJUeN8fv4vcEKr3DEeKmHrm7GSy108YrogB0bG+vX/i2t7azdYmsN/sWdJxAfGw3AabnpIQvW4L9XuGK81ENXN+OlFrp4RXTALi8v92v/ytpGWtraSRsYz+Ckvix/7Ezyztufhy8J7fsSf73CFeOlHrq6GS+10MUroufDzs7O9mv/qp22lodDB9j6Wg/p35ebT5/od778xV+vcMV4qYeubsZLLXTxiugadklJiV/7b925B4AhA6ydz9pf/PUKV4yXeujqZrzUQheviA7YbW1tfu3vCNhDwyxg++sVrhgv9dDVzXiphS5eER2wc3Jy/Nq/pGInAGkDE6zIjmX46xWuGC/10NXNeKmFLl7KBWwrB04pLCzs9b4vf1PqnD5zyuhBfufFSvzxCmeMl3ro6ma81EI1r64GTlGu0Zl7R3J/GD58eK/3feWbUsDW//rYicOsypIl+OMVzhgv9dDVzXiphWpeeXl5zkqpa9BWroYdDmzcvpslpduJjhLMv+MEEuKUu+8xGAwGg2JEdMCurKzs1X4f/bwJKeGMA0cypH94NTiD3nuFO8ZLPXR1M15qoYuXx4AthEgXQswRQiwSQjQIIaQQIsObAwohooQQtwkhyoQQe4QQy4QQ53pIl28/rvvnRv+UvGfy5Mm92m/+sgoATj1ghIW5sY7eeoU7xks9dHUzXmqhi1dXNeyxwPnADuA7H495H5AHPAFMB34E3hFCnOIh7a/AYW6ft3w8X68pKiryeZ8N2+r5evkWooTg+Jy0AOTKf3rjpQLGSz10dTNeaqGLV1cvX7+VUg4FEEJcBZzozcGEEKnALcDfpJSP2Fd/LYQYC/wN+Mxtlzop5Y++Z9saoqOjfUovpeQvr/8CwDEThpISgqkzvcFXL1UwXuqhq5vxUgtdvDzWsKWU7b083klALPCa2/rXgBwhxOheHjcgZGVl+ZT+4Y+W8+kvtjFp779wSiCyZAm+eqmC8VIPXd2Ml1ro4mV1o7OJQBOw1m39cvvPCW7rpwghdgohWoQQvwohZlmcn24pLi72Kf3zX60B4OU/HMGkfQYGIkuW4KuXKhgv9dDVzXiphS5eVvdHGgTUys6dpWtctjv4FngdKAGSgcuA54QQw6WU93d1AveO5AAzZ85k9uzZxMbGUl5eTnZ2NiUlJbS1tZGTk0NhYaGzH15lZSWTJ0+mqKiIqqoqtm/fTnFxMenp6TQ3N1NVVUVubi4FBQXEx8eTkZHBypUr6ZeSRsWORhJiBMftN5D8/HwSExNJS0ujpKSEzMxMqqurqa2tde6fnJxMSkoKpaWlZGVlUVFRQX19vXN7SkoKSUlJlJWVMX78eMrKymhsbHRuT01N9dkpOjqahIQE8vPze3TKyMigrq6O6upq5/ZwdcrKymLz5s2sXbtWK6fi4mLa2tpYsWKFVk6Oa2/z5s3U1dVp5VRVVUVycjL5+flaOeXm5rJ582YWL16slVNBQQHbt29n69atYe00Z84c5s6d222AFT0NRGJ/h/0sMFpKWdZD2n8DZ0gph7mtHwusAS6TUr7azf7/AU4Ghkgp6z1s93Av0HtWrFjBhAnulX7PvLOojCufWsjR44fy6W3HWZaHQOCLl0oYL/XQ1c14qYXKXkIIpJQCrH8kvgNIFp2rwY6adQ3d8ybQFwjKwK9VVVVep33kY9tT/RP3D8+W4a744qUSxks9dHUzXmqhi5fVAXs5EAdkuq133Nqs8PI41lWjuyE3N9erdMUbd7CifCcDEmK45oTwb7zgrZdqGC/10NXNeKmFLl5WB+zPgRbgN27rLwGKpZTre9j/N0AjEJROcwUFBV6l+3blVgBOzx1JXEz4dw/w1ks1jJd66OpmvNRCF68uG50JIWbYvzpuTaYLIbYB26SU39jTtAIvSylnAUgpq4QQjwG3CSHqgF+AC4BpwBkuxz4KuBV4HygDBgAz7WlulVLutsywG+Lj471Kt7zcNo3m5IzwbRnuirdeqmG81ENXN+OlFrp4dddK/B235SftP78Bptq/R9s/rtwO1AM3AMOA1cD5UspPXNJUYqvd3wsMxlYr/xW4WEr5pm8KvScjI8OrdCs21QIwcWRywPJiJd56qYbxUg9d3YyXWuji1eUjcSml6OIz1S3N5W77tUkp75dS7iOljJNSTpJSvuuWZq2UcrqUcoQ9TaKU8vBgBmuAlStX9pimvV2yorwWgAnpyYHNkEV446Uixks9dHUzXmqhi1dEz9blzV3X96uqaGhuY2C/WAYlhudQpO7ocjfpjvFSD13djJda6OKlXMAWQiCEcE7u7Q91dXXdbpdScuPLSwA4cr9Uv88XLHryUhXjpR66uhkvtVDNKy8vzxnrXLF6pLOAY+XAKdXV1d1uL6ncxZrKXQA8fsXBlp030PTkpSrGSz10dTNeaqGaV15enrNS6hq0exzpLJyweqSzuro6kpKSutz+xOeruO2NX7jw8AyeveZwy84baHryUhXjpR66uhkvtVDZK5AjnSlFd33zWlrbeWr+agBOmhz+o5u5okufQ3eMl3ro6ma81EIXr4gO2ImJiV1ue/XbUjZu382AhBimT0kPYq78pzsvlTFe6qGrm/FSC128Ijpgp6V1XXP+bpVt7NmbT59Ivzi1XvV356Uyxks9dHUzXmqhi1dEB+ySkhKP66WULFxtC9jHZQ8PZpYsoSsv1TFe6qGrm/FSC128IjpgZ2a6z1FiY3XFLip2NDKkf1+yFRndzJWuvFTHeKmHrm7GSy108YrogN1VU/8vfq0A4PicYURFuc8UGv6o1oXBW4yXeujqZrzUQhcv5QK2lQOn1NbWelz/vf399TQFH4dD116qY7zUQ1c346UWqnl1NXCK6YftoW/eobd/xvJNtXx378lMzhhk2fmChcp9DrvDeKmHrm7GSy1U9jL9sO146psnpWTTdtvsnukpCcHOkiXo0ufQHeOlHrq6GS+10MUrogN2cnJyp3WvfbeOXY0tDOwXS4oik32448lLB4yXeujqZrzUQheviA7YKSkpHZZbWtu59rnFAJx+4MhO7w9Uwd1LF4yXeujqZrzUQheviA7YpaWlHZaf/2oNAEMH9OWJK9WZ7MMddy9dMF7qoaub8VILXbwiOmBnZWV1WP6iqBKAq48bp2ztGjp76YLxUg9d3YyXWujiFdEBu6Kiwvm9rb2dH0u2AfCbo8aEKkuW4OqlE8ZLPXR1M15qoYtXRAfs+vp65/fijbXsamwhY0g/0lP6hTBX/uPqpRPGSz10dTNeaqGLl3IB28qBU3Jzc53fl5bVAHBQ5mC/jxtqXL10wniph65uxkstVPPqauAU5QK2lBIppSUB27VvXvHGWgAm7TPQ7+OGGl36HLpjvNRDVzfjpRaqeeXl5TljnSvKBWwrcW3qX1K5C4D9RgwIVXYsQ5cuDO4YL/XQ1c14qYUuXhEdsB1D1UkpWV5eC8C44f1DmCNrUHUIvp4wXuqhq5vxUgtdvCI6YJeVlQGwdksdVTv3kDqgL2NSE0ObKQtweOmG8VIPXd2Ml1ro4hXRAXv8+PEArNy8E4D99xmodP9rBw4v3TBe6qGrm/FSC128IjpgO+66SrfWATB2mB6PTXS5m3THeKmHrm7GSy108YrogN3Y2AjA+ipbH73MoXoEbIeXbhgv9dDVzXiphS5eER2wHX3z1tlr2KNT9QjYqvU59BbjpR66uhkvtdDFS7mAbeXAKY6+eXsDtvoNzkC9PofeYrzUQ1c346UWqnl1NXBKnxDlp9e4dyT3h9TUVKp2NrKpuoGY6ChtAnZqamqosxAQjJd66OpmvNRCNa+8vDxnpdQ1aCtXw7aS2NhYXvl2HQBHjU+lT7Qev47Y2NhQZyEgGC/10NXNeKmFLl56RKheUl5ezhe/2mZxmTVtXIhzYx3l5eWhzkJAMF7qoaub8VILXbw8BmwhRLoQYo4QYpEQokEIIYUQGd4cUAgRJYS4TQhRJoTYI4RYJoQ4t4u0VwshVgkhmoQQq4UQ1/jh4jPZ2dmUVNiGJD1wjB5D14HNS0eMl3ro6ma81EIXr65q2GOB84EdwHc+HvM+IA94ApgO/Ai8I4Q4xTWREOJq4BngPeBk4B3gSSHE7308X6+5/+0lbK9rAmBYcnywThtwSkpKQp2FgGC81ENXN+OlFrp4ddXo7Fsp5VAAIcRVwIneHEwIkQrcAvxNSvmIffXXQoixwN+Az+zp+gAPAK9KKW93SZcG3CeEeE5K2dIrIy/ZUtvI84t3OJejotQf4cxBW1tbqLMQEIyXeujqZrzUQhcvjzVsKWV7L493EhALvOa2/jUgRwgx2r58GDDEQ7pXgRTgyF6e32sWr9nm/P7IpXr00XOQk5MT6iwEBOOlHrq6GS+10MXL6kZnE4EmYK3b+uX2nxNc0gEU95AuIEgpeW/xRgBuOGU8vzth30CeLugUFhaGOgsBwXiph65uxkstdPGyuh/2IKBWdu4sXeOy3fXnjh7SdcLT5BwzZ85k9uzZxMbGUl5ebmtMVlJCW1sbOTk5FBYWMnz4cAAqKyvJzpnEf36yBex+fdrIz88nPT2d5uZmqqqqyM3NpaCggPj4eDIyMli5ciUZGRnU1dVRXV3t3J6YmEhaWholJSVkZmZSXV1NbW2tc3tycjIpKSmUlpaSlZVFRUUF9fX1zu0pKSkkJSVRVlbG+PHjKSsro7Gx0bk9NTXVa6fJkydTVFREdHQ0ffv21c4pKyuLjRs3snbtWq2ciouLaW5uZsWKFVo5Oa69jRs3UldXp5VTVVUVSUlJ5Ofna+WUm5vLxo0bWbx4sVZOBQUFVFVVsXXr1rB2mjNnDnPnzu0q9NniX08DkdjfYT8LjJZSlvWQ9t/AGVLKYW7rxwJrgMuklK8KIf6K7R12vJRyj0u6PkALcJeU8j4Px/dwL9A77nhrKa/kr2HxQ6cxfGCCJccMF1avXs2+++r11ACMl4ro6ma81EJlLyEEUkoB1j8S3wEki87VYEeNucYlHcDAHtIFjPsvnMIrF6ZqF6zBduepI8ZLPXR1M15qoYuX1QF7ORAHZLqtd7yTXuGSDva+y+4qXUCZPHlyME4TdIyXWujqBfq6GS+10MXL6oD9ObZH2r9xW38JUCylXG9fXgRs7yJdDfCDxfnySFFRUTBOE3SMl1ro6gX6uhkvtdDFq8tGZ0KIGfavjj5P04UQ24BtUspv7GlagZellLMApJRVQojHgNuEEHXAL8AFwDTgDMexpZQtQog7sQ2UshlYYE9zJXC9lLLZSsmuiI6ODsZpgo7xUgtdvUBfN+OlFrp4dddK/B235SftP78Bptq/R9s/rtwO1AM3AMOA1cD5UspPXBNJKZ8WQkjgZuDPwEbgOinlkwSJrKysYJ0qqBgvtdDVC/R1M15qoYtXl4/EpZSii89UtzSXu+3XJqW8X0q5j5QyTko5SUr5bhfneEZKmWVPNy6YwRqguNi9G7geGC+10NUL9HUzXmqhi1dEz9aVnp4e6iwEBOOlFrp6gb5uxkstdPFSLmALIRBCOCf39ofm5qC8Kg86xkstdPUCfd2Ml1qo5pWXl+eMda4oF7CllEgpLQnY//jHP/zPUBhivNRCVy/Q1814qYVqXnl5ec5Y50qPI52FE1aOdGY/XqdfiA4YL7XQ1Qv0dTNeaqGyVyBHOjMYDAaDwRAAtAnYVjwiD+S5eps/4+U/xsv//YyX/xgv//fT1cvb/bR5JN6bRx69fUxizmXOpeq5erufOZc5lzlXaPYzj8QNBoPBYFAM5WrYoc6DwWAwGAzBxFHDVipgGwwGg8EQqZhH4gaDwWAwKIAJ2AaDwWAwKEDEBWwhxEghxLtCiJ1CiF1CiPeFEKPCIF8zhBDvCSE2CCEahRCrhRAPCSGS3NINFEI8J4TYLoTYLYRYIITI8XC8vkKIh4UQlfbjLRJCHO0hXZQQ4jYhRJkQYo8QYpkQ4twAu34uhJBCiPtVdxNCnCKE+FYIUW+/nn4WQkxT3OkIIcR8IUSVEKJOCPGLEOLKQOdXCHG1EGKVEKLJfv1f44dDuhBijj1fDfbrLcNDupB5CCHOEkIstR9vgxDiDiFEt/NAeuMlhDhQCPFvex4ahBAbhRCvCyFGq+zlYZ9b7em+D1cvy3EMfxYJHyABWAMUA2cBZwJFQCnQL8R5+xGYB/wGOAa4Eai1r4+ypxHA90A5cBFwMrbpTrcD6W7He92+/9XAccD7QCMw2S3dA0ATcAtwLPAM0A6cEiDPi4BKQAL3u6xXzg34HdAC/BM4ATgJ+AtwmsJOk+zn/dr+93GC/RwS+H2g8ms/Trs9/bHA/fbl3/fSYyqwFfgM+J89/xke0oXEw36ttAH/tqf7E7AH+Lu/XsAjwA/Atdj+l1wMrASqgZGqermlH4NtGuetwPcetoeFl9WfoJ0oHD7Y5uhuA8a6rBsNtAJ/CnHehnhYd5n9wp1mXz7TvnysS5oBQA3wfy7r9renu8JlXR9sc5N/5LIu1X5R3+N23i+BXwPgOBDYgi14uQdspdyADGz/2G/sJo1STvZjPQg0A4lu6xcBiwKRX/u+VcDLbulewHZzE9MLjyiX71fhObCFzANYCnzjlu4u++9+mJ9env6X7IMtEN2rqpdb+v9hC8L5uAXscPKy+hOUk4TLx15gP3hY/417YYTDBxhvv3AvtS8/D2z2kO5lYIPL8p32CynBLd099gs5zr58qf3449zSXWFfP9pin38DC+zf3QO2Um7AvcBuoG83aZRysh/rEbtXtNv6z4HFgcgvcJR9+QS3dMfidsPTS6euAltIPICR9uWr3dKNxu0Gojde3aTfCjzvsqykF7YnBtuAQXgO2GHpZcUn0t5hT8T2ONyd5cCEIOfFG46x/1xp/9ld/kcJIRJd0q2XUjZ4SBcLjHVJ1wSs9ZAOLPydCCGOxPbE4A9dJFHN7UhgFXChEKJUCNEqhFgrhHD1U80J4CX7z/8TQqQJIZKFEI7Hxf8MUH4n2n+6/64svw7dCJWHx3RSyvVAAwHwFUKMx1bzXOmyWjkvIcRAbNfhbCllTRfJlPPylkgL2IOAHR7W12B7XBs2CCFGYKvFLZBS/mxf3V3+Ya9DT+kGufyslfbbxW7S+YUQIhbb46tHpJSru0immlsaMA54GPgbcCLwBfCEEOIGL/Mabk5IKYuxvU88E9hsz9dc4Bop5VsByq/jp/sxLb0OPRAqj67SOdZZ6iuE6AM8ja1W+rzLJhW9HgZK2Htj6QkVvbyiT7BOZPAee83rQ2zv1q8IcXasYDYQj61hhy5EAUnA5VLK9+3rvrK3bL1NCPF/IcuZHwghxgHvYatlXIPtPf2ZwNNCiD1SytdDmT9Dr3gCOBw4VUrpKegogRDiKGxP6Q7wEIwjgkirYe/Ac026qzvtoCOEiAc+xtYK8iQpZbnL5u7y79juTboal3TJQgjRQ7peI2xd5m7H9r4wzv6INdm+2bEc7UWew82t2v7zC7f184GhwHDUcwJbo7MWbC3dP5FSfiml/CO2HgyPCyGiApBfx+/B/ZhWenkiVB5dpXOss8xXCPE34LfAlVLK+W6bVfN6BtsTgnKX/yN9gGj7cpxLPlTy8ppIC9jL2fs+wpUJwIog56UTQogY4F3gQGzdD4rcknSX/41SynqXdKOFEAke0jWz993OciAOyPSQDqz5nYwB+gKvYbvwHR+wdbnYAeSgntvyHra3o54T2MpimZSyxW39T0AKtvegVufX8bt0/11Z6eWJUHl4TGd/OpOARb5CiNuxdTP8o5TyVQ9JVPMaj+2pj+v/kSOAQ+3ff++SD5W8vCdYrdvC4YOtb3MrMMZlXQa2GsXNIc5bFLZaTCNwXBdpzsLWKvEYl3X9sdX25rism2JPN9NlXR9sDU4+dlmXiu0f091u51kAFFnklYztnaj7RwKv2r8nquYGnGrPxwy39f8DNilcXvnAOiDWbf0b9msz1ur8AjHY3q++6JbuOfvvKra3PvbjdNVKPGQeQCHwtVu6O/Chm1BXXvZtf7Rv+2s3+yvlhef/I4XYxtKYin1sg3D1suITlJOEywfoh+2uuQjbe7kzgGXY/kElhjhvT9kv0vux3TG6fhwXYhSwENgEXIitM38+tkcy7gMivIXtrvMqbC1838XW0f8At3R/s6//k/2ifwpb7fC0APtKOnbrUsoN26AoX9n/sK/B1ujsWbvX5So62Y8/w+7wP/vfyInY3oFK4LFA5df+O2y3X/9TsTW4bAf+4KfLDPb+bf3evnxMqD2AU+zrn7Gnu8l+/If99bJfa+3Af+n8v2SCql5d7JOP54FTwsbLyk/QThQuH2AUtkY1u4A64AO87McY4HyV2S9ST588l3SDsHXsr8HWpeBLYH8Px4sHHsM2UMkeYDEw1UO6aGx3ihuwdYX4FbdaY4B8OwRsFd2w1ZbnYuvf2mw//sUqO9nPMd3+j3Cb/W+kENuoWdGBzC+2keNK7OnWANdacI15+uSHgwdwDrYKQxOwEdtAHNH+emFrQd2ju2peXeyTj+eAHTZeVn7M9JoGg8FgMChApDU6MxgMBoNBSUzANhgMBoNBAUzANhgMBoNBAUzANhgMBoNBAUzANhgMBoNBAf4f6RTKmSPeyvwAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pd.DataFrame(param_vals).plot(subplots=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Plotting the distributions"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "# define the range, it is also the support of z\n",
    "rng = np.linspace(-1, 5, 1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1000,)"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rng.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Prior on $\\bf{z}$: $p(\\bf{z}) = Exp(\\bf{z}; \\lambda=1)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [],
   "source": [
    "p_z = np.exp(-rng) * (rng >= 0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Joint (fixed on data $x^{[0]} = 1.3$)\n",
    "\n",
    "# $p(z, x=x^{[0]}) = p(z)p(x=x^{[0]}|z) = \\sqrt{\\frac{1}{2\\pi}} e^{-z} e^{\\frac{1}{2} (x^{[0]} - z)^2} I(z \\geq 0)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "x_0 = 1.3\n",
    "p_joint = p_z * (1/np.sqrt(2*np.pi)) * np.exp(-0.5 * (x_0 - rng)**2)\n",
    "# plt.plot(rng, p_joint)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.2776449919880252"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.trapz(p_joint, rng)  # integrate to compute area"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## True posterior is just the joint (fixed to the data) divided by the normalization const. obtained above\n",
    "just integrate out along z (rng here)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "p_post = p_joint / np.trapz(p_joint, rng)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## surrogate posterior $q(\\bf{z}) = Exp(\\bf{z}; \\lambda=\\phi)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "q_z = phi * np.exp(-phi*rng) * (rng >= 0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 576x432 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(rng, p_z, label=r'$p(z)\\, (prior\\,on\\,z)$')\n",
    "\n",
    "plt.plot(rng, p_joint, label=r'$p(z, x=x^{[0]})\\,(joint\\,fixed\\,to\\,data)$')\n",
    "\n",
    "plt.plot(rng, q_z, label=r'$q(z)\\,(surrogate\\,posterior)$')\n",
    "\n",
    "plt.plot(rng, p_post, label=r'$p(z|x=x^{[0]})\\,(true\\,posterior)$')\n",
    "\n",
    "plt.xlabel('$z$')\n",
    "plt.ylabel('$dist.$')\n",
    "plt.legend(loc = \"upper right\")\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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